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If p=tan(-(11pi)/(6)),q=tan((21pi)/(4))a...

If `p=tan(-(11pi)/(6)),q=tan((21pi)/(4))and r = cot ((283pi)/(6))`, then which of the following is / are correct ?
1. The value of `pxxr ` is 2.
2. p , q and r are in G . P . Select the correct anwer using the code given below :

A

1 only

B

2 only

C

Both 1 and 2

D

Neither 1 nor 2

Text Solution

Verified by Experts

The correct Answer is:
B
`p=tan((-11pi)/(6))`
`p=-tan(2pi-(pi)/(6))`
`p="tan"(pi)/(6)=(1)/(sqrt(3))`
`q=tan((21pi)/(4))=tan(6pi-(3pi)/(4))`
`q=-"tan"(3pi)/(4)=+"tan"(pi)/(4)=1`
`r=cot((283pi)/(6))=cot(46pi+(7pi)/(6))=cot(pi+(pi)/(6))`
`r="cot"(pi)/(6)=sqrt(3)`
`pxxr=(1)/(sqrt(3))xxsqrt(3)=1`
`therefore` Statement (1) is incorrect.
also `(p)/(q)=(q)/(r)=(1)/(sqrt(3))`
So p , q r are in G.P.
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